nnmt.lif.exp._firing_rates

nnmt.lif.exp._firing_rates(J, K, V_0_rel, V_th_rel, tau_m, tau_r, tau_s, J_ext, K_ext, nu_ext, I_ext=None, C=None, method='shift', **kwargs)[source]

Calculates stationary firing rates for exp PSCs.

Calculates the stationary firing rate of a neuron with synaptic filter of time constant tau_s driven by Gaussian noise with mean mu and standard deviation sigma based on Fourcaud and Brunel [2002], using either a shift of the integration boundaries in the white noise Siegert formula, calling nnmt.lif.exp._firing_rate_shift(), or a Taylor expansion around k = \sqrt{\tau_\mathrm{s}/\tau_\mathrm{m}} of Eq. 4.33 in Fourcaud and Brunel [2002], calling nnmt.lif.exp._firing_rate_taylor().

Parameters:
Jnp.array

Weight matrix in V.

Knp.array

Indegree matrix.

V_0_rel[float | 1d array]

Relative reset potential in V.

V_th_rel[float | 1d array]

Relative threshold potential in V.

tau_m[float | 1d array]

Membrane time constant of post-synatic neuron in s.

tau_r[float | 1d array]

Refractory time in s.

tau_sfloat

Pre-synaptic time constant in s.

J_extnp.array

External weight matrix in V.

K_extnp.array

Numbers of external input neurons to each population.

nu_ext1d array

Firing rates of external populations in Hz.

I_extfloat, optional

External d.c. input in A, requires membrane capacitance as well.

Cfloat, optional

Membrane capacitance in F, required if external input is given.

method{‘shift’, ‘taylor’}, optional

Method used to integrate the adapted Siegert function. Default is ‘shift’.

kwargs

For additional kwargs regarding the fixpoint iteration procedure see nnmt._solvers._firing_rate_integration().
Returns:
np.array

Array of firing rates of each population in Hz.